Isolated qubits are a special class of quantum devices, which can be used to
implement tamper-resistant cryptographic hardware such as one-time memories
(OTM's). Unfortunately, these OTM constructions leak some information, and
standard methods for privacy amplification cannot be applied here, because the
adversary has advance knowledge of the hash function that the honest parties
will use.
In this paper we show a stronger form of privacy amplification that solves
this problem, using a fixed hash function that is secure against all possible
adversaries in the isolated qubits model. This allows us to construct
single-bit OTM's which only leak an exponentially small amount of information.
We then study a natural generalization of the isolated qubits model, where
the adversary is allowed to perform a polynomially-bounded number of entangling
gates, in addition to unbounded local operations and classical communication
(LOCC). We show that our technique for privacy amplification is also secure in
this setting.
